Help with probability problem, please.

ZiZi

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Nov 8, 2013
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Hi, I haven't been able to figure this problem out:

An assembly line supposedly turns out items that have a weight of 100 pounds each but the population standard deviation is known to be 3 pounds.
What is the probability of taking a random sample from this line and finding that its weight is between 97 pounds and 109 pounds?
A) About 34%
B) About 68%
C) About 84%
D) About 16%
E) About 96%

I really just don't know how to get started with this. We've been talking about null and alternate hypothesis, and we've gone over several example problems. But there hasn't been anything like this though, and it's really throwing me off. Normally, I wouldn't worry about it, but this question is asked repeatedly in different ways, such the probability of being over 100 or less than 91.

Anyways, I would really appreciate some help soon. Thanks!
 
Hi, I haven't been able to figure this problem out:

An assembly line supposedly turns out items that have a weight of 100 pounds each but the population standard deviation is known to be 3 pounds.
What is the probability of taking a random sample from this line and finding that its weight is between 97 pounds and 109 pounds?
A) About 34%
B) About 68%
C) About 84%
D) About 16%
E) About 96%

I really just don't know how to get started with this. We've been talking about null and alternate hypothesis, and we've gone over several example problems. But there hasn't been anything like this though, and it's really throwing me off. Normally, I wouldn't worry about it, but this question is asked repeatedly in different ways, such the probability of being over 100 or less than 91.

Anyways, I would really appreciate some help soon. Thanks!
This question is a throwback to find out your "feel" for the normal distribution. Did you learn "empirical rules"?

1 standard deviation: 34% between 0 and 1, or 68% between ± 1 standard deviation.
...................................16% above +1, 16% below -1 standard deviation
...................................84% greater than -1, 84% less than +1 standard deviation
2 standard deviations: 95% between ± 2 standard deviations
3 standard deviations: 99.7% between ± 3 standard deviations

In other words, a very coarse and limited table of the normal distribution.
 
Oh, wow. We didn't even talk about this in class, but I'm familiar with the concept.

So, thanks to your guidance, I was able to research this. So, the answer to this 84% correct?

And then, say if it was asking for the probability of being less than 97, that would be 16%?

I hope I'm on the right track here.
 
Hi, I haven't been able to figure this problem out:

An assembly line supposedly turns out items that have a weight of 100 pounds each but the population standard deviation is known to be 3 pounds.
What is the probability of taking a random sample from this line and finding that its weight is between 97 pounds and 109 pounds?
A) About 34%
B) About 68%
C) About 84%
D) About 16%
E) About 96%

I really just don't know how to get started with this. We've been talking about null and alternate hypothesis, and we've gone over several example problems. But there hasn't been anything like this though, and it's really throwing me off. Normally, I wouldn't worry about it, but this question is asked repeatedly in different ways, such the probability of being over 100 or less than 91.

Anyways, I would really appreciate some help soon. Thanks!
Dr Phil gave "rules of thumb" for these values. More direct would be to use the standard normal distribution. 100- 97= 3 so 97 is one standard deviation below the mean. That gives a "standard" variable of z= (97- 100)/3= -1.00. 109- 100= 9 so 109 is three standard deviations above the mean: z= (109- 100)/3= 3.00. Now use a table of the standard normal distribution. Statistics text books usually have one in an appendix but there is a nice one at http://www.mathsisfun.com/data/standard-normal-distribution-table.html It shows that between 0 and 3, the area under the curve is .499 while the area between -1 and 0 is .341. The probability of being between -1 and 3 (between 97 and 109 in the original problem) is the sum of those.
 
Oh, wow. We didn't even talk about this in class, but I'm familiar with the concept.

So, thanks to your guidance, I was able to research this. So, the answer to this 84% correct?

And then, say if it was asking for the probability of being less than 97, that would be 16%?

I hope I'm on the right track here.
Both Correct. :cool:
 
I did pretty good on this quiz. Thanks for helping me out! :) I appreciate it!
 
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